Risk Bounds for Reservoir Computing

Gonon, Lukas; Grigoryeva, Lyudmila; Ortega, Juan-Pablo

Risk Bounds for Reservoir Computing

Dateien

Gonon_2-1bk1kceuhte259.pdfGröße: 823.13 KBDownloads: 99

Datum

2020

Autor:innen

Gonon, Lukas

Grigoryeva, Lyudmila

Ortega, Juan-Pablo

URI (zitierfähiger Link)

http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1bk1kceuhte259

Link zur Lizenz

CC BY 4.0

Open Access-Veröffentlichung

Open Access Gold

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Journal of Machine Learning Research (JMLR). Microtome Publishing. 2020, 21, 240. ISSN 1532-4435. eISSN 1533-7928

Zusammenfassung

We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems when processing discrete-time inputs under various hypotheses on their dependence structure. Non-asymptotic bounds are explicitly written down in terms of the multivariate Rademacher complexities of the reservoir systems and the weak dependence structure of the signals that are being handled. This allows, in particular, to determine the minimal number of observations needed in order to guarantee a prescribed estimation accuracy with high probability for a given reservoir family. At the same time, the asymptotic behavior of the devised bounds guarantees the consistency of the empirical risk minimization procedure for various hypothesis classes of reservoir functionals.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Reservoir computing, RC, echo state networks, ESN, state affine systems, SAS, random reservoirs, Rademacher complexity, weak dependence, empirical risk minimization, PAC bounds, risk bounds

Zitieren

ISO 690

GONON, Lukas, Lyudmila GRIGORYEVA, Juan-Pablo ORTEGA, 2020. Risk Bounds for Reservoir Computing. In: Journal of Machine Learning Research (JMLR). Microtome Publishing. 2020, 21, 240. ISSN 1532-4435. eISSN 1533-7928

BibTex

@article{Gonon2020Bound-52899,
  year={2020},
  title={Risk Bounds for Reservoir Computing},
  url={https://jmlr.csail.mit.edu/papers/v21/19-902.html},
  volume={21},
  issn={1532-4435},
  journal={Journal of Machine Learning Research (JMLR)},
  author={Gonon, Lukas and Grigoryeva, Lyudmila and Ortega, Juan-Pablo},
  note={Article Number: 240}
}

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URL der Originalveröffentl.

https://jmlr.csail.mit.edu/papers/v21/19-902.html

Prüfdatum der URL

2021-02-18

Universitätsbibliographie

Ja

Begutachtet

Ja